They have won only one of their last eight games in all competitions - against Premier League champions Manchester United.
McLeish knows exactly what Benitez is going through after being in the managerial goldfish bowl at Rangers but believes the Spaniard can cope.
McLeish said: "I think Rafa Benitez is a smart guy who has been in the game a long time and knows the expectation levels at a club like Liverpool, the same as I did at Rangers.
"We are not daft. When you have some results that are against expectations of the fans and what people expect of Liverpool, then you are always going to be under pressure.
"I was no different with the Rangers job but you have just got to keep your focus, your dignity and keep working as best as you know in the game.
"Rafa is a hugely experienced manager with terrific achievements under his belt.
"But you know how fickle a game it is and people don't care about what your history is. It is what happens next and I am sure that is what Rafa will be conscious of."
McLeish added: "I don't want to comment on the plight of another manager but I can empathise with it because I've been there.
"I don't need to tell Rafa he has got to focus on his own thing and be single minded."